Question

find a quadratic polynomial the sum and product of whose zeroes are respectively -3 and 2​

Answer 1

EXPLANATION.

Sum of the zeroes = - 3.

Products of the zeroes = 2.

As we know that,

Sum of the zeroes of the quadratic polynomial.

⇒ α + β = - b/a.

⇒ α + β = - 3. - - - - - (1).

Products of the zeroes of the quadratic polynomial.

⇒ αβ = c/a.

⇒ αβ = 2. - - - - - (2).

As we know that,

Formula of the quadratic polynomial.

⇒ x² - (α + β)x + αβ.

Put the values in the equation, we get.

⇒ x² - (-3)x + (2).

⇒ x² + 3x + 2.

                                                                                                                       

MORE INFORMATION.

Conjugate roots.

(1) = If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) = If D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

Step-by-step explanation:

$\rm \: \alpha \beta = 2 \\ \rm \: \alpha + \beta = - 3$

Formula Used-

$\rm \: {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ \hookrightarrow \rm \: {x}^{2} - ( - 3)x + 2 \\ \color{olive} \hookrightarrow \rm \: {x}^{2} + 3x + 2$